In a sports poll, 53% of those surveyed believe their high school football team will win the state championship. The poll shows a margin of error of +-5 percentage points. Write and solve an absolute value inequality to find the least and the greatest percent of people that think their team will run the state championship.
Hi! I'm in 9th grade and was kinda annoyed by this question but her is what I got:
|p-53| <= 5
Hope this helped "Jack"! :)
48≤p≤58
53 % margin of 5 percentage is what
To find the least and the greatest percent of people that think their high school football team will win the state championship, we need to consider the margin of error of ±5 percentage points.
Let's assume "x" represents the true percentage of people who believe their team will win the state championship. Based on the margin of error, the least percentage would be "x - 5" and the greatest percentage would be "x + 5".
We can write the absolute value inequality as follows:
| x - 53 | ≤ 5
To solve this inequality, we can break it down into two separate inequalities:
1. x - 53 ≤ 5
x ≤ 5 + 53
x ≤ 58
2. -(x - 53) ≤ 5
-x + 53 ≤ 5
-x ≤ 5 - 53
-x ≤ -48
x ≥ 48 (Multiplying by -1, remember to flip the inequality sign)
Combining the two solutions, we find that the least percentage is 48% (x ≥ 48) and the greatest percentage is 58% (x ≤ 58).